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balance (v.): 1570s, "be equal with," from balance (n.). Meaning "bring or keep in equilibrium" is from 1630s; that of "keep oneself in equilibrium" is from 1833. Of accounts, from 1580s. Related: Balanced; balancing. Balanced meal, diet, etc. is from 1908.
compensation (n.): late 14c., "action of compensating," from Latin compensationem (nominative compensatio) "a weighing one thing against another, a balancing," noun of action from past participle stem of compensare (see compensate). Meaning "what is given in recompense" is from c. 1600; meaning "amends for loss or damages" is from 1804; meaning "salary, wages" is attested from 1787, American English. The psychological sense is from 1914.
resign (v.): late 14c., "give up, surrender, abandon, submit; relinquish," from Old French resigner "renounce, relinquish" (13c.), from Latin resignare "to check off, annul, cancel, give back, give up," from re- "opposite" (see re-) + signare "to make an entry in an account book," literally "to mark" (see sign (v.)).

The sense is of making an entry (signum) "opposite" -- on the credit side -- balancing the former mark and thus canceling the claim it represents. The specific meaning of "give up a position" is first recorded late 14c. Sense of "to give (oneself) up to some emotion or situation" is from 1718. Related: Resigned; resigning.
equilibrist: "An acrobat who performs balancing feats, especially a tightrope walker", Mid 18th century: from equilibrium + -ist.